A novel Fourier-Eight-Sensor (F8S) method for separating straightness, yawing and rolling motion errors of a linear slide

A novel method called the Fourier-Eight-Sensor (F8S) method is proposed for the separation of the straightness, yawing and rolling motion errors as well as the profiles of a linear slide. Eight distance sensors are positioned on a vertical stage in two lines parallel to the target profiles with five sensors in the lower row and the other three in the upper row. The outputs of the sensors are fused together at different times to eliminate the dependence of motion errors. The method adopts a two-stage approach. First, the profile faced by the lower row sensors is represented by Fourier series the coefficients of which are obtained by matrix inversion. Then, another Fourier series is used to represent the difference between the two target profiles. By fusing the outputs of the three sensors in the upper row and their corresponding counterparts in the lower row, the coefficients of the Fourier series are determined by the Fourier series based error separation technique. In this way, different error components can be successfully separated from the sensor outputs. The effectiveness of the method is validated by simulation and experiment.